It's not just drugs - they have some wild laws for regular people. Caning for vandalism, including graffiti, as well as many other "crimes". Chewing gum is banned. Not flushing the toilet is illegal. Also, as far as drugs go, they may drug test you as you enter the country and you can be punished if they find any trace.
Source: https://www.goabroad.com/articles/study-abroad/singapore-laws-to-know-before-you-go